Fuzzy Logic Load Forecasting with Genetic Algorithm Parameter Adjustment

100 Pages·2012·4.07 MB·English

by  Craig Stuart Carlson

FUZZY LOGIC LOAD
FORECASTING WITH GENETIC
ALGORITHM PARAMETER
ADJUSTMENT
Craig Stuart Carlson
A dissertation submitted to the Faculty of Engineering and the Built Environment,
University of the Witwatersrand, Johannesburg, in fulfilment of the requirements
for the degree of Master of Science in Engineering.
Johannesburg, 2012
Declaration
I declare that this dissertation is my own, unaided work, other than where speci-
fically acknowledged. It is being submitted for the degree of Master of Science in
Engineering to the University of the Witwatersrand, Johannesburg. It has not been
submitted before for any degree or examination to any other university.
Signed this day of 2012
Craig Stuart Carlson
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Abstract
World-wide pressure on existing power distribution systems calls for action to be
taken in order to curb the energy deficit. The concept of a smart grid can assist
since a significant function is the improvement of energy efficiency in transmission
and usage. This is also known as energy management. Load forecasting can
indirectly aid energy management by raising user awareness to reduce the peak and
total power usage. Load forecasting has been implemented using many different
methods over the years, from statistical methods to computational intelligence
methods. Combinationsofmethodsalsoexisttoenhancetheforecastingcapabilities.
Following from observations made, it was hypothesised that a fuzzy logic load
forecastingalgorithmcouldbeimprovedbyincorporatinganoptimisationtechnique
such as genetic algorithms.
Inordertoobservetheeffectsofageneticalgorithmonafuzzylogicloadforecasting
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system, MATLAB wasusedtoimplementaloadforecastingalgorithmusingfuzzy
logic systems and genetic algorithms. The fuzzy logic systems used the day (week or
weekend), the time of day and the historic power usage to perform the forecasting.
The genetic algorithm adjusted the fuzzy logic parameters to minimise the peak and
total energy errors in a 24 hour period.
Using data from one week prior to the test yielded the most accurate results after
considering varying quantities of input data. The results obtained from five case
studies indicated a good correlation between the forecast and measured values.
Initial results were obtained using a priori knowledge of the behaviour of the
system, then the genetic algorithm was implemented. The full week forecast results
showed an average improvement, for the five cases, of 4.32 and 18.95 times for the
peak energy error and the total energy error respectively. This indicates that the
dissertation hypothesis was proven to be correct.
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To my ever-supportive parents and my loving wife
for your endless support and for constantly pushing me to fulfil my dreams
Acknowledgements
ThisresearchwasperformedundertheauspicesoftheFutureElectricalEngineering
TechnologiesresearchgroupaswellastheControlResearchGroupattheUniversity
of the Witwatersrand, Johannesburg South Africa.
Firstly, and most importantly, thanks are extended to the South African power
producer, Eskom, for without their support and funding this research would not
have been possible. Additional thanks are extended for their generous supply of the
load profile data from the Southern Region (Eastern Cape Province) used in this
research.
Next to my supervisors, Prof. W.A. Cronj´e and Prof. M.A. van Wyk, thank you for
lettingmediscovermyownwaythroughthisbigworldthatispostgraduatelife. You
letmegaintheexperience, disciplineandknowledgerequiredtocompletesomething
of this level in my own time but pushed me in the right direction when I was going
astray. Without your gentle prodding I fear I would still be at the beginning!
Of course, how could I forget my colleagues, friends and family? You have stood by
me through all the highs and lows. You gave me more minds to bounce ideas off.
For this I cannot express enough gratitude.
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Contents
Declaration i
Abstract ii
Acknowledgements iv
Contents v
List of Figures viii
List of Tables xii
1 Introduction 1
2 Background 3
2.1 Current Grid Architecture . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 Overview of a Smart Grid . . . . . . . . . . . . . . . . . . . . . . . . 4
2.3 Overview of Existing Methods of Load Forecasting . . . . . . . . . . 5
2.3.1 Statistical Models . . . . . . . . . . . . . . . . . . . . . . . . 5
2.3.2 Computational Intelligence Models . . . . . . . . . . . . . . . 6
2.3.3 Combination of Methods . . . . . . . . . . . . . . . . . . . . 9
2.3.4 Comparison of Load Forecasting Methods . . . . . . . . . . . 9
3 Development of the Load Forecasting Algorithm 11
3.1 Assumptions and Constraints . . . . . . . . . . . . . . . . . . . . . . 11
3.2 Definition of Performance Criteria . . . . . . . . . . . . . . . . . . . 13
3.3 Outline of the Load Forecasting Algorithm . . . . . . . . . . . . . . 14
3.4 The Fuzzy Logic Systems . . . . . . . . . . . . . . . . . . . . . . . . 15
3.4.1 Fuzzification Process . . . . . . . . . . . . . . . . . . . . . . . 16
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Contents
3.4.2 Fuzzy Inference Engine . . . . . . . . . . . . . . . . . . . . . 17
3.4.3 Defuzzification . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.5 The Genetic Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.5.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.5.2 Chromosome Representation . . . . . . . . . . . . . . . . . . 20
3.5.3 Objective/Fitness Functions . . . . . . . . . . . . . . . . . . . 21
3.5.4 Reproduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.6 Structure of the Load Forecasting Algorithm . . . . . . . . . . . . . 22
4 Algorithm Testing, Results and Analysis 24
4.1 Preliminary Algorithm Testing to Determine Input Requirements . . 25
4.2 Case 1 - Eastern Cape Province in South Africa . . . . . . . . . . . . 26
4.3 Case 2 - East Campus at the University . . . . . . . . . . . . . . . . 28
4.4 Case 3 - Barnato Hall Student Residence at the University . . . . . . 30
4.5 Case 4 - Chamber of Mines Building at the University . . . . . . . . 32
4.6 Case 5 - Single Plug Point with a Variable Load . . . . . . . . . . . 34
4.7 Analysis of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
5 Recommendations for Future Work 38
5.1 Definition of New Performance Criteria . . . . . . . . . . . . . . . . 39
5.2 Using the Mean Absolute Percentage Error . . . . . . . . . . . . . . 40
5.3 Revising the Fuzzy Logic Systems. . . . . . . . . . . . . . . . . . . . 41
6 Conclusion 45
A Detailed Comparison of Load Forecasting Implementations 47
B Important Definitions 51
B.1 Fuzzy Logic Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
B.2 Genetic Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
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C MATLAB Code Listings 55
C.1 Fuzzy Logic System Creation . . . . . . . . . . . . . . . . . . . . . . 56
C.2 Genetic Algorithm Code . . . . . . . . . . . . . . . . . . . . . . . . . 58
C.2.1 Genetic Algorithm Creation . . . . . . . . . . . . . . . . . . . 58
C.2.2 Fitness Functions . . . . . . . . . . . . . . . . . . . . . . . . . 59
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Contents
C.3 Algorithm Initialisation . . . . . . . . . . . . . . . . . . . . . . . . . 62
C.4 Algorithm Calculations and Results . . . . . . . . . . . . . . . . . . 63
D Additional Information for the Case Studies 67
D.1 Case 1 - Eastern Cape Province in South Africa . . . . . . . . . . . . 68
D.2 Case 2 - East Campus at the University . . . . . . . . . . . . . . . . 71
D.3 Case 3 - Barnato Hall Student Residence at the University . . . . . . 74
D.4 Case 4 - Chamber of Mines Building at the University . . . . . . . . 77
D.5 Case 5 - Single Plug Point with a Variable Load . . . . . . . . . . . 80
References 83
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List of Figures
2.1 A representation of the existing power distribution system architecture. 4
2.2 Overview of a typical expert system. . . . . . . . . . . . . . . . . . . 7
2.3 Overview of a general artificial neural network. . . . . . . . . . . . . 8
2.4 Simplified model of an artificial neuron. . . . . . . . . . . . . . . . . 8
2.5 Overview of a Mamdani fuzzy logic system. . . . . . . . . . . . . . . 9
3.1 Sample load profile to illustrate the need to distinguish between (a):
Week and (b): Weekend days in the load forecasting algorithm. . . . 12
3.2 Flow diagram showing the processes for the load forecasting algorithm. 15
3.3 Overview of the fuzzy logic system used in the load forecasting algo-
rithm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.4 Input fuzzy sets for (a): Time and (b): Historic power usage used in
the load forecasting algorithm . . . . . . . . . . . . . . . . . . . . . . 17
3.5 Output fuzzy set used in the forecaster. . . . . . . . . . . . . . . . . 18
3.6 Illustrationofthemeanofmaximumdefuzzificationcalculation. Time
= 10h00; Historic power usage = 10 kWh; Predicted power usage
(after defuzzification) = 9.9 kWh. . . . . . . . . . . . . . . . . . . . . 19
3.7 Overview of a conventional genetic algorithm. . . . . . . . . . . . . . 19
3.8 Structure of the load forecasting algorithm (in black) and the accom-
panying performance evaluation and optimisation processes (in grey). 23
4.1 (a): Input to the load forecasting algorithm and (b): Full week
forecast for the Eastern Cape Province in South Africa. . . . . . . . 27
4.2 (a): Input to the load forecasting algorithm and (b): Full week
forecast for East Campus at the University. . . . . . . . . . . . . . . 29
4.3 (a): Input to the load forecasting algorithm and (b): Full week
forecast for the Barnato Hall student residence at the University. . . 31
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List of Figures
4.4 (a): Input to the load forecasting algorithm and (b): Full week fore-
cast for the Chamber of Mines engineering building at the University. 33
4.5 (a): Input to the load forecasting algorithm and (b): Full week
forecast for a single plug point with a variable load. . . . . . . . . . 35
5.1 Structure of the revised load forecasting algorithm (in black) and the
accompanying performance evaluation and optimisation processes (in
grey). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
5.2 Flow diagram showing the proposed logic for the revised load fore-
casting algorithm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
B.1 Illustration of a universe of discourse, a fuzzy membership function
and the degree of membership. . . . . . . . . . . . . . . . . . . . . . 51
B.2 Illustration of parental crossover in genetic reproduction. . . . . . . . 54
B.3 Illustration of mutation of a chromosome on the fifth gene. . . . . . 54
D.1 Map of South Africa (taken from Google Earth) showing the area the
load profile was taken from, for the Eastern Cape Province test. . . . 68
D.2 NormalisedloadprofileandthepredictedpowerusagefortheEastern
Cape Province for a general Monday. . . . . . . . . . . . . . . . . . . 68
D.3 NormalisedloadprofileandthepredictedpowerusagefortheEastern
Cape Province for a general Tuesday. . . . . . . . . . . . . . . . . . . 69
D.4 NormalisedloadprofileandthepredictedpowerusagefortheEastern
Cape Province for a general Wednesday. . . . . . . . . . . . . . . . . 69
D.5 NormalisedloadprofileandthepredictedpowerusagefortheEastern
Cape Province for a general Thursday. . . . . . . . . . . . . . . . . . 69
D.6 NormalisedloadprofileandthepredictedpowerusagefortheEastern
Cape Province for a general Friday. . . . . . . . . . . . . . . . . . . . 70
D.7 NormalisedloadprofileandthepredictedpowerusagefortheEastern
Cape Province for a general Saturday. . . . . . . . . . . . . . . . . . 70
D.8 NormalisedloadprofileandthepredictedpowerusagefortheEastern
Cape Province for a general Sunday. . . . . . . . . . . . . . . . . . . 70
D.9 Map of Main Campus at the University showing the area the load
profile was taken from, for the East Campus test. . . . . . . . . . . . 71
D.10Normalised load profile and the predicted power usage for East Cam-
pus at the University for a general Monday. . . . . . . . . . . . . . . 71
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